let p, q be Element of MC-wff ; :: thesis: ( p 'or' q in IPC-Taut iff q 'or' p in IPC-Taut )

hereby :: thesis: ( q 'or' p in IPC-Taut implies p 'or' q in IPC-Taut )

assume A1: p 'or' q in IPC-Taut ; :: thesis: q 'or' p in IPC-Taut
(p 'or' q) => (q 'or' p) in IPC-Taut by Th56;
hence q 'or' p in IPC-Taut by A1, Def14; :: thesis: verum

end;

assume A2: q 'or' p in IPC-Taut ; :: thesis: p 'or' q in IPC-Taut
(q 'or' p) => (p 'or' q) in IPC-Taut by Th56;
hence p 'or' q in IPC-Taut by A2, Def14; :: thesis: verum